I am speculating, but I believe that the General controls most of the country as well as the oilfilds, pipelines and even loading docks. He does not control the capital, where an International-backed faction still holds sway. The reason he can't just do what he wants with the oil is that international players won't allow loading of (what they consider) rogue cargoes. So the General has physical control, but has to allow a significant amount of the funds to go to the Tripoli faction. And then it's actually more complicated since there's two different factions left in Tripoli. And even the General is actually running a coalition of factions.But I could be wrong.
I certainly don't have any idea what's going on in Libya. But it certainly doesn't seem to have an adverse effect on price of oil.